Three solid cubes have a face diagonal of 4√2 cm each. Three other solid cubes have a face diagonal of 8√2 cm each. All the cubes are melted together to from a big cube. Find the side of the cube formed (in cm).
A
10
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
12
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
13
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
15
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is B12 Face of a cube is a square. Diagonal of a square =√2×side So, for Cube 1: √2×side1=4√2 =>Side1=4cm And for Cube 2 √2×side2=8√2 =>Side2=8cm So, total volume of all 6 cubes melted =3(Volume of cube_1) +3(Volume of cube_2) =3×43+3×83=1728 cu. cm. As one large cube is formed with this volume, we have
(Side of large cube)3=1728 ⇒ Side of large cube =12 cm.